Additional Examples of sample spaces and events
Example 1:
In the experiment of tossing a single regular sixsided die, there are six possible outcomes.
Thus the sample space is
Ω={
,
,
,
,
,
}.
This may also be depicted simply as
Ω={
1, 2, 3, 4, 5, 6}.
Let A be the event that even number of spots
turn up, i.e.
A
={
,
,
}.
Or
A={2,4,6}. A is an event; that is it consists of a subset of elementary outcomes in Ω.
Since in this
example the sample space is finite, the
event space,
sometimes denoted by
A.
, consists of all subsets of
Ω. Thus, there are
6
2
=64 events, of which only 6 are elementary, in
A.
, including both
φ
and
Ω.
Example 2:
Toss a penny, nickel, and a dime simultaneously, not whether heads
(H) or tails (T ) is up.
There are eight possible outcomes of this experiment; thus Ω={(H,H,H), (H,H,T), (H,T,H), (T,H,H), (H,T,T),
(T,H,T),(T,T,H), (T,T,T)}. We are using the first posi
tion of the
3tuple
(∙,∙,∙) to record the outcome of the
penny, the second position to record
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 Spring '11
 Zhou
 Probability theory

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